UNloaded beam size for 20' span

I plan to erect an 18 foot by 20 foot pergola over my patio. The 18 foot span is between my house and my shop. I will uses PT 2x10s spaced 15" on center as joists between the two structures to provide partial shade. The joists will be attached and supported by the two structures. I intend to support the 2x10s with a pressure treated pine 4x12 or 4x14 central beam that will be supported by 6x6 posts 20' apart. I don't expect a live load (no snow here). Is a 4x12 or 4x14 Pressure treated Pine adequate for my central beam?